## Copyright (C) 2003 Gabriele Pannocchia
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} isdefinite (@var{x}, @var{tol})
## Return 1 if @var{x} is symmetric positive definite within the
## tolerance specified by @var{tol} or 0 if @var{x} is symmetric
## positive semidefinite.  Otherwise, return -1.  If @var{tol}
## is omitted, use a tolerance equal to 100 times the machine precision.  
## @end deftypefn
##
## @seealso{issymmetric}

## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
## Created: November 2003
## Adapted-By: jwe

function retval = isdefinite (x, tol)

  if (nargin == 1 || nargin == 2)
    if (nargin == 1)
      tol = 100*eps;
    endif
    sym = issymmetric (x, tol);
    if (sym > 0)
      ## Matrix is symmetric, check eigenvalues.
      mineig = min (eig (x));
      if (mineig > tol)
	retval = 1;
      elseif (mineig > -tol)
	retval = 0;
      else
	retval = -1;
      end
    else
      error ("isdefinite: matrix x must be symmetric");
    endif
  else
    usage ("isdefinite (x,tol)");
  endif

endfunction